A two-phase multi-fidelity framework for virtual sensing of a rotating shaft system with physics-informed machine learning

Abstract

This paper proposes a physics-informed machine learning framework for virtual sensing in the unmeasurable regions of a rotating shaft system. This framework addresses the challenge of predicting dynamic responses in regions where direct sensor installation is difficult or infeasible, thereby enabling real-time full-field virtual sensing under diverse operating conditions. The proposed framework comprises two sequential phases with distinct objectives. First, a physics-guided multi-agent diverse generative adversarial network (PhyMAD-GAN) synthesizes high-fidelity full-field synthetic responses under specific operating conditions by integrating full-field low-fidelity data from multiphysics finite element analysis (FEA) with point-wise measurements. The PhyMAD-GAN employs multiple generators to enhance synthetic data diversity, a shared discriminator to ensure consistency with measurements, and a physics-guided loss to preserve physical constraints. Second, a physics-informed adversarial domain-adaptive deep operator network (PADO-NET) constructs a generalized surrogate model that performs virtual sensing across both trained and untrained operating conditions. PADO-NET integrates operator learning to represent nonlinear mappings, domain-adversarial alignment to extract domain-invariant features, and physics-informed regularization to supervise governing physics laws. Extensive validation using dynamic responses, measured from an induction motor testbed under diverse operating conditions, confirmed the effectiveness of the proposed framework. The systematic analysis demonstrated significant improvements in predictive accuracy, robustness, and generalization compared with conventional data-driven neural networks. The proposed framework contributes to the artificial intelligence transformation of mechatronic systems by enabling reliable full-field virtual sensing. This capability provides physically consistent and reliable full-field reconstructions of shaft dynamics, which are essential for intelligent condition monitoring and fault diagnosis.